Continuous Blood Pressure Measurement

ABSTRACT

We disclose a system and method for estimating values of hemodynamic parameters of a subject, by calibrating arterial pressure during one time and tracking arterial pressure at another time.

RELATED APPLICATIONS

U.S. provisional application 62/609,435 titled “Estimating therelationship between MAP value and pulse amplitude and methods toachieve so,” is hereby incorporated herein by reference.

BACKGROUND Field of the Invention

This invention relates to measurement of human blood pressure values(BPVs). Sphygmomanometers, tonometers, and Penaz devices, for measuringblood pressure, are known. See for example U.S. Pat. No. 5,579,776(cuff); U.S. Pat. No. 6,413,223 (tonometer); and U.S. Pat. No. 9,107,588(Penaz device). Hemodynamic parameters include Mean Arterial Pressure(MAP), Pulse Pressure (PP), Systolic pressure (Ps), Diastolic pressure(Pd), and Stroke Volume Variation (SVV).

A medical practitioner normally uses a manual sphygmomanometer and astethoscope to determine Ps and Pd. A convention formula for estimatingMAP from Ps, and Pd is:

MAP=⅔Pd+⅓Ps  (1)

Oscillometric cuff based sphygmomanometers may determine MAP, Ps, and Pddirectly from pressure data without using this formula.

A cardiac cycle is the sequence of events that occurs when the heartbeats. There are two phases of the cardiac cycle. In the diastole phase,the heart ventricles are relaxed and the heart fills with blood. In thesystole phase, the ventricles contract and pump blood out of the heartand to arteries. Arterial pressure waves resulting from one cardiaccycle include a first segment associated with systole followed by asecond phase associated with diastole. The second phase typicallyincludes a dicrotic notch, so that the arterial pressure wave associatedwith each cardiac cycle has two maxima, one on either side of thedicrotic notch.

Definitions

Herein after “subject” means human or mammal.

Herein after, an “arterial pulse” means the signal associated with thepressure variation over time of one complete cardiac cycle.

Hereinafter, a “cardiac time period” means a time period correspondingto an individual arterial pulse. The cardiac time period is alsoreferred to herein after as the InterBeat Interval, and as IBI.

Hereinafter, a processing system defines a system that can implementalgorithms for processing signals obtained from biometric transducers.

A processing system comprises a processing unit and memory. Theprocessing unit may be virtualized in which case it is stored ascomputer code in memory. Thus, both the processing unit and the memoryare implemented using hardware. Hardware refers to physical componentsthat alter electrical or optical signals, such as resistors, capacitors,inductors, diodes, transistors, light emitting diodes, and lasers.Preferably, a processing system comprises a digital processing systemwhich processes digital data. Digital data refers to discrete ordiscontinuous representation of information. Preferably, both theprocessing unit and the memory of a digital processing system eachcomprise at least one digital electronic integrated circuit.Alternatively, a digital processing system may be implemented withphotonic computing components. A processing unit could also comprises ananalog processing unit. The processing unit of a processing system maycomprises components that are remotely located from one another. Memoryof a processing system may also comprise components that are remotelylocated form one another.

Hereinafter, “F( . . . )” means “a function of” the elements listedwithin the parenthesis. This does not mean the each recitation “F( . . .)” refers to the same function.

Hereinafter, SV is an acronym for Stroke Volume. Stroke Volume means thevolume of blood ejected from a ventricle of a heart of a subject duringone cardiac cycle.

Hereinafter, a tracking sensor means any biometric transducer and acompatible front end capable of providing a signal comprising pluralsampled values correlated to arterial pressure change of some regionwithin the subject, during each cardiac cycle.

Hereinafter, when describing Fourier transform of a real valued signal,the description relates to the positive frequencies only.

Stroke Volume Variation, SVV, is a measure of variation in SV from twoor more cardiac cycles.

A cardiovascular model is a model that relates blood flow (in volume pertime) to blood pressure of a subject.

Electrical model means a model in the form of a mathematical descriptionof an electrical equivalent circuit that represents the behavior of anelectrical system.

SUMMARY OF THE INVENTION

We disclose blood pressure measurement systems and methods using atracking transducer and tracking transducer front end, for tracking asubject's BPVs over an extended period of time. These blood pressuremeasurement systems and methods enable tracking BPVs for each arterialpulse. Preferably, the tracking transducer does not restrict blood flowand is not within the body. The tracking transducer provides atransduced signal to the tracking transducer front end. An output of thetracking transducer front end provides a signal that is correlated toarterial pressure in the region of the subject from which the trackingtransducer obtains signal. Herein after, a tracking sensor refers toboth the tracking transducer and the tracking transducer front end. Thetracking sensor is capable of providing plural values correlating toarterial pressure during a single cardiac cycle. (For example, pluralsampled values of a continuous signal at several times during a singlecardiac cycle to provide plural values during a cardiac cycle.)

The transducer typically includes a plurality of LED's for generatinglight to transmit to a blood vessel to be measured, and a pin diodeacting as an optical to electrical transducer converting the receivedlight to an electrical signal. A front end circuit amplifies, filtersand samples the signal from the tracking sensor transducer. The frontend outputs a sequence of values corresponding to the value output fromthe tracking sensor transducer over time. The sampling frequency must behigh enough so that the cardiac cycle can be distinguished. Thissampling frequency must be at least 4 Hertz (Hz), preferably greaterthan 10 Hz, more preferably greater than 32 Hz. The sampling frequencyis preferably less than 1 terahertz, and more preferably less than10,000 Hz, and still more preferably less than 1,000 Hz. A practicalupper limit to the sampling frequency is determined by the response timeof the sensor, the duty cycle required to obtain a reasonable signal tonoise ratio, and the upper frequency at which the sensor componentsrespond. This limit may be about 10 GHz. If conductive cabling is usedto carry the sensor signal to remote processing circuitry, signaldispersion in the cabling may result in a sampling frequency upper limitof 1 GHz.

The tracking sensor may comprise a PPG (photoplethysmography)transducer, reflective or transmissive, Electromagnetic wave sensor,RADAR sensor, a bioimpedance sensor, a pressure sensor like anapplanation tonometer, or an ultrasonic sensor. The tracking sensor maybe mounted, implanted, or positioned adjacent any location of the bodyof the subject where the output of the sensor correlates to arterialpressure These locations include but are not limited to the wrist,finger, arm, torso, leg, foot, head, forehead, earlobe, nose, and cheek.

In the preferred embodiment, the tracking sensor comprises a standardfingertip PPG transducer clipped or secured to a tip of a finger of thesubject. PPG transducers are typically used for determining a subject'soxygen saturation level. Typically, PCMs (Patient Care Monitors) obtainsignals from PPG sensors (for determining a subject's oxygen saturationlevel) at a sampling rate of between 100 and 200 Hz. Typical PPG sensorstransduce signals at 660 nm and 940 nm, and combine the magnitude ofboth transduced signals within the sensor to provide a single sensoroutput signal. Embodiments use the signal received in a PCM from a PPGtransducer as the tracking signal. For this reason, embodimentscontemplate arterial pressure at 100 to 200 Hz. Embodiments employ aPCM, modified to perform the signal processing disclosed herein, forcalibration and monitoring. These PCMs may also include a port forreceiving data from one of the aforementioned types of calibrationsensors. Disclosed methods comprise normalizing MAP, Ps, Pd arterialpressures data from the tracking sensor (tracking data), using valuesfor MAP, Ps, and Pd, derived from a calibration sensor.

The calibration sensor is designed to provide signals from which a valuefor MAP and a value for PP (the difference between the Systolic pressureand the Diastolic pressure) for a subject can be determined. Sensorsthat provide such signals and can function as the aforementionedcalibration sensor are well known, and include sphygmomanometers,tonometers, and Penaz devices. The calibration sensor may also comprisea pressure transducer inside an artery, or connected via a fluid filledtube to an artery.

Disclosed methods also comprise determining from the tracking data, timeperiods corresponding to individual cardiac cycles.

Disclosed methods comprise, performing a DFT on tracking data for acardiac pulse.

Disclosed methods comprise replacing a DC value for the DFT spectrum ofan arterial pulse obtained from a tracking sensor, with some nonzerovalue.

Disclosed methods comprise replacing a DC value for the DFT spectrum ofan arterial pulse obtained from a tracking sensor, with values derivedfrom the calibration sensor and the DFT of the tracking data.

Disclosed methods comprise determining from data provided by thetracking sensor, and a calibration, MAP, systolic (Ps), and Diastolic(Pd) pressures, on a pulse by pulse basis.

In a first aspect, we provide systems and methods for using the systemsfor estimating values of hemodynamic parameters of a subject,comprising: a processing system comprising a processing unit and memory;wherein the processing system is designed to receive calibration sensordata that relates to arterial pressure from a calibration sensor;wherein the processing system is designed to receive tracking sensordata from a tracking sensor; the processing system is designed tocalculate estimated hemodynamic values of a hemodynamic parameter basedupon: one or more outputs of a DFT of tracking sensor data relating tothe arterial pressure, and which tracking sensor data was obtained fromthe subject during a calibration time period; at least two of MAP, PP,Ps, and Pd values from data obtained from the subject during thecalibration time period; one or more outputs of a DFT of tracking sensordata relating to the arterial pressure, which tracking sensor data wasobtained during a tracking time period; and wherein the tracking timeperiod is different from the calibration time period; wherein theprocessing system is designed to display, store or transmit theestimated hemodynamic values.

Dependent features of this first aspect include: wherein the processingsystem is designed to calculate an FSUB value for an FSUB function;wherein FSUB is a function of variables comprising: MAP; PP; and a valueof a harmonic of a DFT of tracking sensor dat; and wherein theprocessing system is designed to determine parameters of a fittingfunction by fitting the fitting function to another function of outputof a DFT of tracking sensor data, for data obtained from the subjectduring the calibration time period; and wherein a parameter of thefitting function depends upon MAP; and wherein the processing system isdesigned to determine parameters of a fitting function by fitting thefitting function to another function of output of a DFT of trackingsensor data, for data obtained from the subject during the tracking timeperiod; and wherein the processing system is designed to hold constantthe value of at least one determined parameter that was determined fromdata obtained from the subject during the calibration time period, whenfitting tracking data during the tracking time period; and wherein theprocessing system is designed to calculate a value for MAP that relatesto blood pressure of the subject during the tracking time period, fromvalues for parameters calculated during the calibration time period, andtracking sensor data obtained from the subject during the tracking timeperiod; and wherein the processing system is designed to calculate avalue for MAP that relates to blood pressure of the subject during thetracking time period, from data also comprising the value for MAPobtained from the subject during the calibration time period; whereinthe processing system is designed to determine a value for MAP bycomputations comprising computing the function

MAPest=MAPcalib*P(w0est)/Q(w0est)*Q(w0calib)/P(w0calib), where:

P represents a polynomial; Q represents a polynomial; w0est is a modelparameter; w0Calib is a model parameter; and MAPcalib is a value for MAPobtained during a calibration time period; and wherein the processingsystem is designed to calculate a value for MAP by computationscomprising computing the function MAPest=MAPcalib*w0est**2/w0calib**2,where: w0est is a model parameter; w0calib is a model parameter; andMAPcalib is a value for MAP obtained during a calibration time period;and wherein the processing system is designed to calculate a PP trackingvalue for PP from values for parameters determined during thecalibration fitting and the tracking fitting, and the value for PPobtained during that calibration time period; and wherein the processingsystem is designed to determine a PP tracking value for PP from valuesfor parameters determined during the calibration fitting and thetracking fitting, the value for PP obtained during that calibration timeperiod, and the value of at least one arterial time period during thecalibration time period and the value of at least one arterial timeperiod during the tracking time period; and wherein system furthercomprises: a calibration sensor; a tracking sensor; and a device forvisually displaying or transmitting values for hemodynamic parameters;and wherein the processing system is designed to compute values from (1)values of a DFT of tracking sensor data and (2) a value for FSUBcalculated using MAP; PP; and a value of a harmonic of a DFT of thattracking sensor data; and wherein said processing system stores acombined electrical model that corresponds to a cardiovascular model;wherein said combined electrical model comprises a current source; aload; and at least one two-port network; and an equipotential potentialconnection between output of said current source and input of both saidload and said at least one two-port network; and wherein said combinedelectrical model comprises a second two-port network that has anequipotential connection to an output of said least one two-portnetwork; and wherein said processing system stores an electrical modelthat comprises a series connection of an inductor and capacitor, andcapacitance of said capacitor is proportional to 1/MAP; and wherein saidprocessing system stores an electrical model that comprises atransmission line, and a parameter of said transmission line is afunction of MAP.

In a second aspect, we provide systems and methods for using the systemsfor estimating a ratio of SV values of a subject, comprising: aprocessing system comprising a processing unit and memory; wherein theprocessing system is designed to receive tracking sensor data from atracking sensor data that relates to changes in arterial pressure; theprocessing system is designed to estimate a ratio of SV values, basedupon: one or more outputs of a DFT of tracking sensor data relating tothe arterial pressure; and wherein the processing system is designed tostore or transmit said ratio of SV values.

Dependent features of this second aspect include: wherein the processingsystem is designed to determine parameters of a combined electricalmodel that corresponds to a cardiovascular model, by a calibrationfitting of a function of the combined electrical model to a function ofoutput of a DFT of tracking sensor data for data from a calibration timeperiod; and wherein the system further comprises a calibration sensor; atracking sensor; and a device for visually displaying or transmittingvalues for hemodynamic parameters; and wherein the processing system isdesigned to determine SVV from ratio of SV values.

In a third aspect, we provide systems and methods for using the systemsfor estimating values of hemodynamic parameters of a subject,comprising: a processing system comprising a processing unit and memory;wherein the processing system is designed to determine a calibrationvalue for at least of MAP, PP, Ps, and Pd from calibration sensor dataobtained from a subject; wherein the processing system is designed tocalculate an FSUB value from a function of variables comprising: MAP;PP; and a value of a harmonic of a DFT of tracking sensor data obtainedfrom the subject; wherein the processing system is designed to calculatehemodynamic values of at least one hemodynamic parameter using said FSUBvalue and said calibration value; and wherein the processing system isdesigned to store or transmit the calculated hemodynamic values.

In a fourth aspect, we provide systems and methods for using the systemsfor estimating values of hemodynamic parameters of a subject,comprising: a processing system comprising a processing unit and memory;wherein the processing system is designed to receive tracking sensordata from a tracking sensor; wherein the processing system is designedto calculate estimated hemodynamic values of a hemodynamic parameter attwo or more time instances, based upon: one or more outputs of a DFT oftracking sensor data relating to the arterial pressure, which trackingsensor data was obtained from the subject during a first tracking timeperiod;

-   -   one or more outputs of a DFT of tracking sensor data relating to        the arterial pressure, which tracking sensor data was obtained        from the subject during a second tracking time period; wherein        the first tracking time period and the second tracking time        period do not overlap in time; and wherein the processing system        is designed to display, store or transmit data relating to the        estimated hemodynamic values. The dependent aspects are        generally interchangeable with and applicable to all independent        aspects.

Summary of Blood Pressure Measurement Systems

The term “blood pressure measurement system” refers to a processingsystem, at least one biometric tracking sensor, means (wires, fiberoptics, or wireless transmitters and receivers) for the sensor tocommunicate data to the processing system, and at least one outputdevice (monitor, audio generator, etc.). The output device can be usedto display time dependent data, sound an alarm, or perform a similarfunction, or control some other system, dependent upon results ofprocessing of received data. The hardware includes at least one digitalprocessing unit and one digital memory unit for storing digital data.The processing system is configured to perform a calibration using datafrom both sensors. The first sensor, or calibration sensor, providesmeasurements from which MAP and PP can be determined. The trackingsensor, or tracking sensor, provides a time dependent signal correlatedto the arterial blood pressure.

The processing system inputs temporally correlated outputs of the twosensors to determine calibration parameters useful in subsequentlytracking the blood pressure over time based solely upon the output ofthe tracking sensor. Subsequent to determining the calibrationparameters for a subject, the processing system can then be used totrack blood pressure over time for that subject, using the input fromonly the tracking sensor.

As part of the calibration, the processing system performs a DFT of asignal from the tracking sensor, for a time interval segmentcorresponding to the time for one complete cardiac cycle. The processingsystem then applies a DC component estimating function to: (1) the valuefor the first harmonic output by the DFT and (2) a ratio of MAP/PP. TheDC component estimating function generates a substitute DC componentvalue. In subsequent steps of the calibration, the processing systemuses this substitute DC component value instead of the zeroth orderharmonic output by the DFT.

Summary of Methods

A cardiovascular model can be described with an analogous electricalmodel, in which current corresponds to blood flow and voltagecorresponds to blood pressure.

We disclose methods comprising two generic steps. First, the processingsystem performs a calibration. The calibration involves data obtainedfrom two sensors measuring certain biometric data from the same subject,calibration data from a calibration sensor, and tracking data from atracking sensor.

The processing system uses that data to determine values for parametersof an electrical model, for that subject. Second, the processing systemuses (1) the values for MAP and/or PP from the calibration; (2) valuesfor parameters of that electrical model for that subject obtained by thecalibration; and (3) values of the electrical model obtained by fittinga combined electrical model representing the cardiovascular system and atracking sensor to the tracking sensor output, to output estimates ofvarious values of hemodynamic parameters. These may include: MAP; PP;Ps; Ps; SV; and SVV. The processing system may also estimate hemodynamicparameters during both the first and second steps by using parametersdetermined for the electrical model and MAP and/or PP.

The design of the cardiovascular model described below indicates that,once calibrated for a particular subject, the outputs of the systemusing the cardiovascular model calibrated for that particular subjectshould be accurate for extended periods of time. Current data resultsshow accuracy for a subject exists for a period of weeks. Significantly,the time period over which the model's tracking is accurate for asubject is much longer than the time typically required for a medicalprocedure, thereby allowing these embodiments to use a singlecalibration and then accurately monitor the arterial pressure of asubject for the duration of a medical procedure. However, for anysubject, the calibration step may be repeated at any time to ensurecontinued accuracy and reliability of tracking of arterial pressurevalues for that subject. For example, the calibration may be repeatedevery: few minutes; fifteen minutes; half hour; hour; half day; day;week; month; or longer.

Summary of Calibration

FIG. 7 shows algorithm 700 comprising steps of calibrating 701 andtracking 702. Arrow exiting 702 and entering 701 indicates that thecalibrating followed by tracking may be repeated. Repeating may occuronce, aperiodically, or periodically, for example at intervals between 1minute and twelve months. Number of repetitions may be zero, that is,only one calibration may ever be performed. Preferably, the systeminitially performs on a particular subject at least 3 or 4 calibrationsclosely spaced in time, such as at intervals of 1-3 minutes, followed bycalibrations at larger time intervals, such as between ever 15 and 60minutes. Calibrating step 701 and tracking step 702 are described hereinbelow.

FIG. 17 shows flow chart 1700 comprising steps 1710 to 1770, describedbelow.

First, Positioning

First, in step 1710, a calibration sensor and a tracking sensor are eachpositioned relative to a particular subject so that these sensors canobtain biometric signals from that subject. The tracking transducer islocated at a position relative to the subject where it can detect anarterial pulse to provide tracking data. Such locations include adjacentthe wrist, finger, arm, torso, leg, foot, head, forehead, earlobe, noseala or cheek. In a preferred embodiment, the tracking transducer isplaced on a fingertip.

Second, Obtaining Data from Both Sensors

Second, in step 1720, a processing system obtains sensor measurementsfrom both the calibration sensor and the tracking sensor. Preferably,the processing system obtains sensor measurements from both sensors thatoverlap in time. The smaller the time difference between the signalsfrom the tracking sensor and the calibration sensor that are used by theprocessing system to perform calibration, the higher the anticipateddegree of accuracy for the resulting calibration. Preferably, theprocessing system stores sensor measurements in memory.

The third and fourth steps can occur in any order, but must occur beforethe fifth step.

Third, Determining Values from Calibration Sensor

Third, in step 1730, the processing system determines a value for MAPand a value for the ratio of PP/MAP, based upon signals sensed by thecalibration sensor over a period of time. This determination may be madeby circuitry adjacent the sensor's transducer or remote from thesensor's transducer. The processing system stores these values inmemory.

The tracking sensor is designed to provide a time dependent signal thatcorrelates with the time dependent arterial pressure wave at the regionof the subject's arteries from which the tracking sensor receivessignals.

Fourth, Processing Tracking Sensor Data

Fourth, in step 1740, the processing system separates the signals fromthe tracking sensor into discrete time interval segments. Each discretetime interval segment corresponds to the time for one cardiac timeperiod. These discrete time interval segments each comprise a set ofsampled values representing the particular cardiac cycle.

The processing the system determines characteristic features in thesignal from the tracking sensor which it assumes corresponds to thebeginning and end of a cardiac cycle. For example the system maydetermine times of local maxima for the signal, the time of maximalderivative within some timeframe, and the second time derivative of thesignal from the tracking sensor, and use any one or more of thesecharacteristic features to indicate end of one cardiac cycle andbeginning of the next cardiac cycle. The processing system may alsoinclude identifying the extrema of a correlation of a predefinedfunction to the signal from the tracking sensor, to determine start andend of each cardiac cycle.

In the preferred embodiment, the processing system takes tracking datafrom a tracking sensor for an arbitrary time period, and determines thearterial pulses contained within that period. The processing systemtakes the segments of the beginning and end of that arbitrary timeperiod which it determines are not part of a complete pulse in thatarbitrary time period. The tracking system connects these segments tothe adjacent time period, so that all pulses are accounted for.

The system performs a Discreet Fourier Transform (DFT) on each discretetime interval segment, to provide the DFT values and correspondingfrequencies, for each discrete time interval segment. This DFT resultsin values for the first and subsequent harmonics for that discrete timeinterval, H0, H1, H2, H3, etc., for each discrete cardiac time period.For calibration, it is only essential to perform DFT on values for onediscrete time interval segment corresponding to one arterial pulse.However, it may be useful to perform this DFT on plural arterial pulsesand use values from these plural arterial pulses. Because the durationof cardiac cycles vary from one another, it is important to retain theactual frequency values for each cardiac cycle, or equivalently, thetime interval duration. Instead of retaining the actual frequencyvalues, the processing system could store the time interval duration, ornumber of samples associated with each time interval duration.

A result of the fourth step is a frequency domain representation of thetracking signal, for each arterial pulse. The processing system storesfrequency domain representation of the tracking signal, for eacharterial pulse, in memory.

However, it is also possible, although less preferred, for theprocessing system to perform DFT on a discrete time segment equal to aplural cardiac cycles. (In this alternative, a corresponding electricalmodel is designed to represent the corresponding arterial pressureresulting from this plural of arterial pulses. The electrical modelcorresponding to one arterial pulse is discussed below.)

Fifth, Determine Estimated Hos of Arterial Pulses

Fifth, in step 1750, the processing system calculates a value for a DCcomponent estimating function, FSUB. FSUB may be a function of thevalues, H1, H2, H3, etc., for DFT of the discrete time interval segment;and the MAP and PP values derived from the calibration sensor.

The DC component estimating function outputs a real number. The DCcomponent estimating function may have the form:

FSUB=F(H1,H2,H3, . . . ,MAP,PP) where FSUB is a real number.

FSUB must be a function of at least MAP, PP (from the calibrationsensor's data), and at least one of the values for H1 to H10.

In some embodiments

FSUB=F(MAP,PP,and H1)=H1*{K*(MAP/PP)+ξ*MAP}, where:  (2)

ξ is in the range of −0.2 to 0.2; and

K is between 3 and 8.

Preferably, K is 5.56 plus or minus thirty percent, and in a preferredembodiment is 5.56. Preferably, ξ is between −0.01 and 0.01, and morepreferably zero.

The absolute value of FSUB/H1 of a subject varies between 1 and 100.This ratio changes for each cardiac cycle of a subject, and also differssubject to subject. (FSUB is real. H1 may be complex.) The processingsystem stores the calculated values for the DC component estimatingfunction, FSUB, for pulses, in memory.

Sixth, Normalize the Dft of the Values Obtained from the TrackingSensor, Using the Value Determined for Fsub

Sixth, in step 1760, the processing system divides the values for H1,H2, H3, etc. of the DFT from the tracking signal for one arterial pulse,by the value for FSUB, and preferably stores the results in memory. Thisnormalizes H1, H2, H3, etc., for the tracking signal, to the FSUB value.This provides a normalized output MEASURE1. MEASURE1 does not include avalue for the zero harmonic (corresponding to a DC value in timedomain). MEASURE1 includes the normalized values of H1, H2, H3, etc.

Seventh, Fitting Output of a Model to the Normalized Output

An output of such an analogous electrical model (corresponding to acardiovascular model) represents arterial pressure in the region of thesubject sensed by the tracking transducer. An output of a combinedelectrical model combining such an electrical model and a model of atracking sensor coupled to arterial pressure at some location in asubject, provides an output of the tracking sensor.

The processing system is configured to determine parameters of acombined electrical model by fitting the model to normalized output.

In some embodiments, the electrical model comprises a model timeconstant, τ, which models a time constant of a cardiovascular system. Insome embodiments, the electrical model comprises a parameter Ts, whichrepresents a time difference between when Systole begins and adetermined time at which the corresponding cardiac cycle begins.

MODEL1 is the combined electrical model normalized by multiplying valuesof the output of the combined electrical model by a constant such thatthe value at zero frequency of the resulting MODEL1 is unity.

Seventh, in step 1770, the processing system performs a fitting between(1) the output of MODEL1 and (2) MEASURE1. This fitting is performed byminimizing differences between two functions evaluated at one of more ofthe harmonic frequencies H1, H2, H3, etc., preferably evaluated at leasttwo harmonic frequencies, and in a preferred embodiment at the H1, H2,and H3 frequencies. Fitting provides one set of parameters of the modelfor whatever frequencies are evaluated. One function is the output ofthe combined electrical model. The other function is the MEASURE1. Thedomain values for each function are the same harmonic frequenciesdetermined for the corresponding arterial pulse.

Fitting of the combined electrical model to the MEASURE1 results invalues of parameters of the electrical model. The processing systemstores these values of parameters of the electrical model in memory.

The processing system may perform the foregoing minimization for aplurality of arterial pulses time correlated to when the processingsystem used data from the calibration sensor to obtain MAP and/or PPvalues. The processing system may use one or more of the sets ofparameters obtained by these minimizations to arrive at representativevalues for these parameters. For example, the processing system maydiscard or reduce the weight of parameters that are relatively extremecompared to corresponding values from other arterial pulses.Consequently, for each calibration relying upon a MAP and/or PP value,the processing system determines one final set of parameters for theelectrical model.

Fitting, such as least squares fitting and algebraic fitting are old andwell known in the art. Fitting minimizes some measure of the differencebetween two functions over an interval, such as the square of thedifference of the functions at each point. Algorithms to fit functionsto data signals are old and well known. The fitting results in valuesfor the parameters of the electrical model that are specific to theparticular subject from which the data was received. These personalmodel parameter values result in a model calibrated to that subject.Determining a subject's personal model parameter values completes thecalibration, for that subject, and for the specific MAP value obtainedfrom the calibration sensor. Conventional numerical method is used toperform the fitting.

In some embodiments, the processing system minimizes error function,“err”, which is defined as follows (and is a measure of the differencein values of the combined electrical model to the MEASURE1):

$\begin{matrix}{{{err} = {W \circ {{abs}\left( {\frac{{MODEL}_{1}(H)}{{MEASURE}_{1}(H)} - 1} \right)}}},} & (3)\end{matrix}$

H=1, 2, . . .

where “∘” represents the dot product operator;

H represents the harmonic number; and

W is a weighting function. W may have values (1; 0.5 to 15; 0.3 to 50,and any real number for higher harmonics). Preferably, W has values inthe range (1; 0.5 to 5; 2 to 20, and any real number for higherharmonics). W may have values: (1, 1, 1); (1, 2, 4); (1, 1.2, 4); (1,1.2, 6); (1, 1.3, 9); (1, 1.2, 12); and (1, 1.1, 14), and zero for allhigher harmonics.

The interval of time over which the data from the tracking sensor wasused in the calibration does not necessarily have to overlap with theinterval of time over which the calibration sensor data was used todetermine a value for MAP. For example, if the subject's arterialpressure variations over cardiac cycles remain very stable over time,then offsets in the time intervals for obtaining a MAP value and thetime interval for obtaining the data from the tracking sensor used inthe calibration may not substantially change the resulting determinationof parameters of the model. However, the closer in time to one anotherare those two time intervals, the more accurate calibration of themodel. Preferably, the interval of time over which the data from thetracking sensor was used in the calibration and the interval of timeover which the calibration sensor data was used to determine the valuefor MAP have at least some overlap. More preferably, interval of timeover which the data from the tracking sensor was used in the calibrationand the interval of time over which the calibration sensor data was usedto determine the value for MAP overlap have greater than a 50 percentoverlap, even more preferably a 90 percent overlap, and most preferablyare (within the accuracy of sampling rates for the sensors) identical.

Thus, the seventh step results in representative values of parameters ofthe electrical model obtained using data for one or more arterialpulses.

The processing system may implement an algorithm to perform a qualitycheck on tracking sensor signal to reject outlier arterial pulses fromuse in calibration.

Consequently, the calibration of the model is completed when one set ofparameters for the electrical model based upon MAP and/or PP valuesprovided by the calibration sensor is completed.

Tracking Arterial Pressure

After a calibration is completed for a particular subject, the systemcan use (1) the values for parameters of the electrical model stored inmemory during calibration; (2) the MAP and/or PP values stored in memoryduring calibration; and (3) the signal from the tracking sensor, toestimate arterial pressure values versus time, for that subject. Theprocessing system continuously receives data from the tracking sensor,and performs pulse by pulse operations to estimate MAP and/or PP on apulse by pulse basis. Pulses in this paragraph refer to arterial pulses.Pulse by pulse herein indicates that the processing system estimatesvalues for MAP and/or PP on individual pulses. Optionally, theprocessing system estimates other hemodynamic parameters using the pulseby pulse determinations. The processing system may store in memory,transmit, or both, the resulting estimate MAP and/or PP, and estimatearterial pressure values versus time.

After calibration, the tracking sensor remains in a position capable ofdetecting arterial pressure. As in calibration step 2, the trackingprovides a time dependent signal that correlates with the time dependentarterial pressure wave at the region of the subject's arteries fromwhich the tracking sensor receives signals

During tracking, as in the fourth step of calibration, the processingsystem separates the signals from the tracking sensor into discrete timeinterval segments. Each discrete time interval segment corresponds tothe time for one complete cardiac cycle. These discrete time intervalsegments each comprise a set of sampled values representing theparticular cardiac cycle. The system performs a Discreet FourierTransform (DFT) on each discrete time interval segment, to provide theDFT values and corresponding frequencies, for each discrete timeinterval segment. This DFT results in values for the first andsubsequent harmonics for that discrete time interval, H0, H1, H2, H3,etc, for each cardiac time period. Because the duration of cardiaccycles vary from one another, it is important to retain the actualfrequency values for each cardiac cycle, or equivalently, the timeinterval duration. Instead of retaining the actual frequency values, theprocessing system could store the time interval duration, or number ofsamples associated with each time interval duration.

A result of the fourth step is a frequency domain representation of thetracking signal, for each arterial pulse. However, as in calibration, itis also possible, although less preferred, for the processing system toperform DFT on a discrete time segment equal to a plural cardiac cycles.(In this alternative, a corresponding electrical model is designed torepresent the corresponding arterial pressure resulting from this pluralof arterial pulses. The electrical model for one arterial pulse isdiscussed below.)

Preferably, the processing system uses no more than the first fiveharmonics in normalization and/or fitting; preferably the processingsystem only uses data for harmonics below 20 Hz.

FIG. 18 shows a flow chart 1800 showing steps for tracking arterial dataincluding steps 1810 to 1880.

At 1810, the processing system may determine which normalization to use.

The following two alternatives for performing normalization and fittingare described:

First Normalization and Fitting Method

First Normalization

During tracking, at 1820, as in the fifth step in calibrating, theprocessing system calculates a value for a DC component estimatingfunction, FSUB, for at least one arterial pulse, and preferably for allarterial pulses.

FSUB may be a function of the values, H1, H2, H3, etc., for DFT of thediscrete time interval segment; and the MAP and PP values previouslyderived from values determined by the calibration sensor. For eacharterial pulse, the processing system determines an FSUB value. Theprocessing system divides values for H1, H2, H3, etc., of that arterialpulse, by this FSUB value for that arterial pulse. This results innormalized harmonic values for the corresponding arterial pulse.

Alternatively to using a single pair of MAP and PP values from onecalibration, the processing system may calculate average values for MAPand PP from plural calibrations, or may calculate weighted averagevalues for MAP and PP from plural calibrations. For each arterial pulse,the processing system then uses these average values of MAP and PP, andthe corresponding H1, H2, H3, etc., values for that arterial pulse, todetermine a value for FSUB for that pulse. The processing system thendivides the values for H1, H2, H3, etc., of that arterial pulse, by thisFSUB value for that arterial pulse. This results in normalized harmonicvalues for the corresponding arterial pulse.

First Fitting using as MODEL1

During tracking, at 1830, similar to the seventh step of calibrating,the processing system performs a fitting between (1) the output ofMODEL1 and (2) normalized harmonic values for the corresponding arterialpulse, at the harmonic frequencies for that arterial pulse. Hereinafter, the normalized harmonic values for the corresponding arterialpulse, at the harmonic frequencies for that arterial pulse, are referredto as “MEASURE1”

The processing system performs the fitting by minimizing differencesbetween the MEASURE1 and MODEL1. The differences may be calculated atone or more of the harmonic frequencies H1, H2, H3, etc., preferably attwo or more harmonic frequencies, and in a preferred embodiment atharmonic frequencies H1, H2, and H3.

The particular electrical model employed for calibration and fittingcontains plural parameters. During the fitting occurring for tracking,some parameters of the electrical model that were determined during thecalibration process, are held constant.

Preferably, τ and Ts are held constant during fitting for tracking.

Fitting of the MODEL1 to MEASURE1, for an arterial pulse, results invalues of parameters of the MODEL1, for that arterial pulse. The resultof this fitting are multiplicity of sets of values of parameters forMODEL1, one set per arterial pulse.

Second Normalization and Fitting Method

Alternatively to the First Normalization, at 1860, the processing systemperforms a second Normalization.

Second Normalization

Unlike during calibration, the processing system does not normalize tothe DC component of the calibration signal. Instead, the processingsystem divides the value for H1, H2, H3, etc. of the DFT from thetracking signal for arterial pulse, by the magnitude of the value forH1. This normalizes H1, H2, H3, etc., for the tracking signal. Hereinafter, these normalized values and corresponding frequencies are called“MEASURE2.” MEASUSRE2 values may be complex. The magnitude of thefundamental harmonic of MEASUSRE2 is by definition unity (H1 divided bythe magnitude of H1).

Second Fitting

During tracking, at 1870, similar to the seventh step of calibrating,the processing system performs a fitting between the output of acombined electrical model, referred to herein after as MODEL2, andMEASURE2.”

MODEL2 is the combined electrical model normalized by multiplying valuesof the output of the combined electrical model by a real valued constantsuch that the magnitude of its first harmonic value is unity.

The processing system performs fitting on a predefined number ofharmonics, excluding the zero (DC) Harmonic. The processing system maycalculate differences at one or more of the harmonic frequencies H1, H2,H3, etc, preferably at two or more harmonic frequencies, and in apreferred embodiment at harmonic frequencies H1, H2, and H3. In apreferred embodiment, the processing system performs fitting at H1, H2,and H3.

The particular combined electrical model employed for calibration andfitting contains plural parameters.

For this second fitting alternative, some parameters of the electricalmodel that were determined during the calibration process, are heldconstant for fitting during tracking. Preferably, τ and Ts are heldconstant during this fitting.

Fitting of the MODEL2 to MEASURE2, for an arterial pulse, results invalues of parameters of the MODEL2, for that arterial pulse. The resultof this fitting are multiplicity of sets of values of parameters forMODEL2, one set per arterial pulse. In some embodiments, fitting ofMODEL2 TO MEASURE2 uses an error function like “err” except that MODEL2and MEASURE2 replace MODEL1 and MEASURE1.

The processing system may use the values of a parameters of a model, foran arterial pulse, and that model, to estimate values representingbiometric parameters of the subject. These include Ps, Pd, MAP, SV perarterial pulse, diameter, length, and stiffness of the Aorta, and heartpumping energy per arterial pulse, heart elastance, heart unloadedvolume, end-systolic volume, and end-diastolic volume.

Eighth, Estimating MAP

At 1840, the processing system uses one of the following twoalternatives for estimating MAP:

First Method of Estimating MAP

The processing system estimates one or more values for MAP, for anarterial pulse, to be the result of a function of values comprisingvalues for w₀calib; MAPcalib; and w₀est. One such estimate of MAP for apulse is MAPest, which is defined as follows:

MAPest=F(w ₀calib;MAPcalib; and w ₀est).  (4)

w₀calib is the representative value of one particular model parameterobtained from fitting during a particular calibration. The phrase“representative value” in this paragraph refers to the representativevalues discussed for the seventh step of calibration.

MAPcalib is the value for MAP obtained during calibration for thatparticular calibration.

w₀est is the value of the same particular electrical model parameterobtained from fitting of tracking data for an arterial pulse.

Preferably, the processing system estimates MAPest by computing a valuefor the function:

MAPest=MAPcalib*P(w ₀est)/Q(w ₀est)*Q(w ₀calib)/P(w ₀calib).  (5)

P represents a polynomial.

Q represents a polynomial.

In one embodiment,

P(x)=K2*x**2+K3x**3 and Q(x)=K4, where K2, K3, and K4 are coefficients,and “**” means “to the power”. K2, K3, and K4 have predetermined fixedvalues.  (6)

In a currently preferred embodiment,

P(x)=x*x and Q(x)=1. In this embodiment, K2=1,K3=0 and K4=1.  (7)

K2, K3, and K4, may be subject dependent. For subject dependence, theprocessing system may determine K2, K3, and K4 by determining values forK2, K3, and K4, that minimizes error between measured MAPest determinedusing different calibrations. For example, differences for values ofMAPest for an arterial pulse, as determined by different MAPCalib valuesfrom different calibrations may be calculated, and then squared. Theprocessing system may then determine K2, K3, and K4 values that minimizethat sum. This process may be extended to data for values of MAPest forplural arterial pulses.

Another estimate of MAP for an arterial pulse is MAPout(n), which isdefined below.

The processing system may filter MAPest outliers. For example, theprocessing system may filter MAPest to compute MAPout(n). For example,by performing the following exponential filter on values for MAPout.

MAPout(n)=ff*MAPout(n−1)+(1−ff)*MAPest(n)  (8)

Where: n is an index that identifies a sequence of arterial pulses;MAPout(n) is the output of the function for the nth arterial pulse; ffis a forgetting factor whose value is between 0 and 1 and preferablybetween 0.8 and 0.98; and most preferably between 0.9 and 0.95; MAPout(n−1) is the value of MAPout for the pulse n−1; and MAPest(n) is thevalue for MAPest for pulse n.

The processing system may filter the input value to MAPout by removingvalues of MAPest that are outliers. That is, suspect due to theirrelatively large difference from some normative value or range for MAP.

Second Method of Estimating MAP

The processing system estimates one or more values for MAP, for anarterial pulse, to be the result of a function of values comprisingvalues for a multiplicity of calibrations w₀calib[i]; MAPcalib[i]; andw₀est, where i=1, . . . , n. One such estimate of MAP for a pulse isMAPest2, which is defined as follows:

MAPest2=F(w ₀calibs;MAPcalibs;and w ₀est), where:  (9)

w₀calibs is a vector, that is a series of values w₀calib[i], i=1, . . ., n;

MAPcalibs is a vector, that is a series of values MAPcalib[i], i=1, . .. , n; and

w₀est is defined above.

w₀calib[i], i=1, . . . , n are each a representative value of oneparticular model parameter obtained from fitting for each one of the ncalibrations. The phrase “representative value” in this paragraph refersto the representative values discussed for the seventh step ofcalibration.

Preferably, the processing system estimates MAPest2 by computing a valuefor the function:

MAPest2=(P(w ₀est)/Q(w ₀est)) times: AVG(MAPcalib[i]*Q(w ₀calib)/P(w₀calib)).  (10)

AVG( ) is an operator representing weighted averaging

P and Q each represent a polynomial and w₀est and w₀calib are definedabove. (Polynomial Q does not represent the same quantity as Q specifiedas a parameter of an electrical described herein.)

In one embodiment:

P(x)=K2*x**2+K3x**3 and Q(x)=K4, where K2, K3, and K4 are coefficients;and “**” means “to the power”; K2, K3, and K4 have predetermined fixedvalues; and  (11)

AVG=(1/n)*(sum(MAPcalib[i]*(w ₀calib)/P(w ₀calib))), where “sum( )”means the sum of all elements in the argument.  (12)

In a currently preferred embodiment,

P(x)=x*x and Q(x)=1. In this embodiment, K2=1, K3=0 and K4=1;  (13)

AVG(x)=ff2*x[−n]+ff2**2*x[n−1]+ . . . +ff2**n*x[1], where:  (14)

** stands for “to the power of” and ff2 is a number between 0 to 1.Preferably ff2 is between 0.3 to 0.7 an more preferably ff2 is between0.45 to 0.55  (15)

Another estimate of MAP for an arterial pulse is MAPout2(n), which isdefined below.

The processing system may filter MAPest2 outliers. For example, theprocessing system may filter MAPest2 to compute MAPout2(n). For example,by performing the following exponential filter on values for MAPout2.

MAPout2(n)=ff*MAPout2(n−1)+(1−ff)*MAPest2(n)  (16)

Where: n is an index that identifies a sequence of arterial pulses;MAPout2(n) is the output of the function for the nth arterial pulse; ffis a forgetting factor whose value is between 0 and 1 and preferablybetween 0.8 and 0.98; and most preferably between 0.9 and 0.95;MAPout2(n−1) is the value of MAPout2 for the pulse n−1; and MAPest2(n)is the value for MAPest2 for pulse n.

The processing system may filter the input value to MAPout2 by removingvalues of MAPest2 that are outliers. That is, suspect due to theirrelatively large difference from some normative value or range for MAP.

Ninth, Estimating PP

At 1850, the processing system performs one of the followingalternatives for estimating PP.

First PP Estimation Method:

The first PP estimation method estimates the PP of a particular arterialpulse.

This particular pulse is called the estimated arterial pulse. The firstPP estimation method estimates PP2 of the particular arterial pulse froma function of the PP of another arterial pulse. This equation is:

$\begin{matrix}{{{PP}\; 2} = {{PP}\; 1*\frac{{MAP}_{2}}{{MAP}_{1}}*\sqrt{\frac{\left( {\tau_{1}*w_{1}} \right)^{2} + 1}{\left( {\tau_{1}*\frac{{MAP}_{2}}{{MAP}_{1}}*W_{2}} \right)^{2} + 1}}}} & (17)\end{matrix}$

where:

PP2 is the PP of the particular arterial pulse; PP1 is the PP of theother arterial pulse; MAP2 is a value for MAP of the particular arterialpulse determined in the eighth step; MAP1 is the MAP of the otherarterial pulse;

$\begin{matrix}{{w\; 1} = \frac{2*\Pi}{IBI_{1}}} & (18) \\{{w\; 2} = \frac{2*\Pi}{IBI_{2}}} & (19)\end{matrix}$

τ₁ is a time constant that can be calculated by:

$\begin{matrix}{{\tau_{1} = \sqrt{\frac{{K^{2}*\left( \frac{{MAP}_{1}}{{PP}_{1}} \right)^{2}} - 1}{w_{1}^{2}}}},} & (20)\end{matrix}$

where K is the constant defined above

Where: Π is the mathematical constant (ratio of circumference todiameter); “j” is the imaginary number (square root of minus); IBI₁ isthe cardiac time period of the other arterial pulse; and IBI₂ is thecardiac time period of the particular arterial pulse.

PP2 is the estimate of PP resulting from the first PP estimation method.

Second PP Estimation Method

The second PP estimation method estimates the PP of the particulararterial pulse, from a function of the PP of another arterial pulse, asfollows:

using a different equation:

PP2=PP1*MAP2/MAP1, where:  (21)

PP2 is the estimate of PP for the particular arterial pulse; PP1 is thePP of the other arterial pulse; MAP2 is the MAP of the particulararterial pulse determined in the eighth step; and MAP1 is the MAP of theother pulse.

PP2 is the estimated PP resulting from the second PP estimation method.

Tenth, at 1880, the processing system estimates Ps and/or Pd.

The processing system may estimate Ps and/or Pd from PP and MAP usingfunctions of MAP and PP. Generally:

Ps=F(MAP,PP); and

Pd=F(MAP,PP).

The conventional choices for these two functions are:

Ps=MAP+⅔*PP  (22)

Pd=MAP−⅓*PP.  (23)

In one embodiment, MAP is the result of eighth step, and PP is theresult of the ninth step.

SV determination and SVV Estimation

FIG. 19 shows a flow chart 1900 containing steps 1910-1980, describedbelow, for estimating SV.

The processing system determines a relative value for SV on a pulse bypulse basis. The ratio of SV for any two pulses is a measure of SVV.Statistical variations in plural SVs can be determined by ratios of SVsfrom plural pulses. These statistical variations are measures for SVV.Typically, SVV refers to a normalized standard deviation representingstandard deviation of SV for a number of arterial pulses, divided by themean of these SVs. The processing system determines a value for SVV bycalculating this normalized standard deviation.

The processing system determines a relative value for SV on a pulse bypulse basis, as follows. After acquiring tracking data for a period oftime corresponding to a sequence of arterial pulses, as discussed above,the processing system uses characteristic features in the signal todetermine times corresponding to the start time for each one of a trainof arterial pulses.

The processing system determines coefficients of a model where a forcingfunction is used as the system excitation. The forcing functionrepresents current in an electrical model and corresponds to blood flowexiting the heart of a subject. The coefficients correspond to theeffect of the transmission of the blood from the heart to the positionfrom which the tracking sensor obtains data. The processing systemequates the linear combination of coefficients and values of a forcingfunction to the tracking data. The forcing function and the trackingdata may be represented in either time domain or frequency domain. Theunknowns in the equations are the (real number) values for the SVs. Theresult in either case is a series of coupled linear equations, which canbe solved in a conventional manner, to determine relative values for thesequence of SVs. The model assumes that there is a fixed (that is pulseindependent), but unknown time difference, between times at which acharacteristic feature (e.g., maxima, or maxima in some power of thederivative) exists in the forcing function and the cardiac cycle starttimes. Requiring SVs to be real enables this time difference to bedetermined and the equations to be solved. Solving in the frequencydomain is preferred, but the processing system could also solve in timedomain. The solution process for SV below relies on linear algebra, anduses matrix inversion to solve the set of equations formulated below.Other methods such as Gaussian elimination, Kramer's method, LUdecomposition, Levinson recursion, etc. may also be used.

SV estimation step 1: At 1910, the processing system determinessequential cardiac cycle start times in tracking sensor data. Theprocessing system selects n adjacent start times. These start times are:T1, T2, . . . , Tn. The total duration of the n cardiac cycles defines atime segment, Tseg=T(n+1)-T(1). The corresponding sequence of SVs arereferred to herein below as SV(i), for i=1 to n.

At 1920, SV estimation step 2: At 1920, the processing system Fouriertransforms the tracking sensor data for a period of time correspondingto a sequence of arterial pulses. The result of this step are a seriesof values and corresponding frequencies. The frequencies are 0, 1/Tseg,2/Tseg, . . . .

SV estimation step 3: At 1930, the processing system selects nfrequencies to be used in the SV estimation, where n is the number ofcardiac cycles determined in SV estimation step 1. Preferably, the nfrequencies are [(n−n//2)/Tseg, (n−n//2+1/Tseg, . . . n/Tseg(n+1)/Tseg .. . (n+n//2−1)/Tseg)] where the symbol “//2” means “integer division,”by 2, which is division by 2 in which any remainder is ignored.

SV estimation step 4: At 1935, the processing system evaluates thefrequency response of some electrical model representing therelationship between SV and arterial pressure of a subject. Preferably,this electrical model is the electrical model used for calibration.Preferably, the parameters in this electrical model are the parametersdetermined during from calibration when fitting the output of theelectrical model to the normalized output MEASURE1. The processingsystem evaluates this electrical model at the frequencies determined inSV estimation step 3. The results are values of the frequency responseat these frequencies.

SV estimation step 5: At 1940, the processing system divides each valueof the Fourier transform obtained from SV estimation step 2 by thecorresponding model response value. The result is an ordered sequence ofn values that are a ratio of the actual data divided by model data forthe n frequencies determined in step 2. Call this ordered sequencevector “R.”

SV estimation step 6: At 1950, the processing system determines thevalues of an n by n matrix M. The first row of Matrix M contains valuesthat are the Fourier Transform of a sequence of Dirac delta functions ata first frequency w1, of the

n frequencies selected in SV estimation step 3. The first row and firstcolumn element of M, is M(1,1). M(1,1) stores the value of the FourierTransform of the first Dirac delta function at frequency w1. M(1,2)stores the value of the Fourier Transform of the second Dirac deltafunction at frequency w1, etc. M(2,1) stores the value of the FourierTransform of the first Dirac delta function at frequency w2. M(2,2)stores the value of the Fourier Transform of the second Dirac deltafunction at frequency w2, etc. M(n,n) stores the value of the FourierTransform of the last Dirac delta function at frequency wn. M(i,k)stores exp(−j*Tk*wi).

In the preferred embodiment the processing system inverts this matrix Mto determine matrix invM.

SV estimation step 7: At 1970, the processing system determines a value,deltaT, which minimizes the imaginary part of Z in the matrix equation:

Z=invM*invL(deltaT, . . . )*R, where:  (24)

Z is n by 1 matrix of complex values;  (25)

invL is an n by n diagonal matrix having matrix values exp(j*deltaT*w1)at position 1, 1; exp(j*deltaT*w2) at position 2,2, . . . ,exp(j*deltaT*wn) at position n,n; deltaT is an unknown having a realvalue; and R is the ordered sequence vector defined above.

Preferably, the processing system performs a minimization algorithm thatminimizes an error function that is a function of the values of thecomponents of Z, to determine the value of deltaT. However, deltaT mayalso be determinable by direct solution methods, for example linearalgebra methods. One suitable error function is:

Err=sum(im(Z(i)**2) where:  (26)

“**” means “to the power”;

im( ) means the imaginary part;

sum( ) means the sum of all the arguments; and

Z(i) is ith value for Z.

Suitable minimization algorithms are well known, and include L-BFGS-B,Nelder-Mead, Powell, conjugate gradient, BFGS, Newton-conjugategradient, truncated Newton algorithm, Constrained Optimization BY LinearApproximation, Sequential Least Squares Programming, and DifferentialEvolution.

The result of SV estimation step 7 is a value for deltaT.

SV estimation step 8: At 1980, the processing system substitutes thevalue for deltaT found in SV estimation step 7 in invL as defined in SVstep 7, calculates

SV=real(invM*invL*R), where:  (27)

SV is an ordered sequence of the components SV(i), i=1 to n;

real( ) is an operator that determines the real part of each of theargument's components; and R the ordered sequence vector defined above.

The processing system can use the values of the components of SV tocalculate SVV.

Fitting to Tracking Data Spanning Plural Cardiac Cycles

The processing system can perform DFT of tracking data for a discretetime segment equal to plural cardiac cycles. In this case, the drivingfunction of the electrical model represents the driving function havingthat plurality of pulses. Each one of these cardiac cycles has aspecific SV associated with it. In this case, the processing system mayuse the SV estimation method to set the amplitude of the drivingfunction for each pulse.

Preferred System and Method

A preferred method uses an automated Sphygmomanometer to measure Ps andPd of a subject. Automated Sphygmomanometer typically use anoscillometric method for measurement. Automated Sphygmomanometerspressurize and then depressurize a cuff, or vice versa, and takemeasurements of blood pressure as the cuff deflates or inflates.Automated Sphygmomanometers determine one value for Ps, one value forPd, and one value for MAP, based upon data captured during cuffinflation or deflation, which occurs over a series of (more than one)cardiac cycles. The time period over which a an automatedSphygmomanometer takes data to determine a value for Ps, or for Pd, orfor MAP (or any combination of such values), is normally on the order often seconds, which normally corresponds to about 10 cardiac cycles ofthe subject.

Preferably, a tracking sensor provides a tracking signal from the samesubject during the time period over which the Sphygmomanometer receivesdata from which the Sphygmomanomete determines Ps, Pd, and/or MAP forthat subject.

Preferably, a single device hardware receives both the automatedSphygmomanometer's data and the tracking sensor's signal. In oneembodiment, the single hardware device is a PCM. Conventional PCMstypically receive various biometric signals measured from a human,including signals indicative of heart beat and blood oxygen level, andprovide a time dependent visual display of those biometric parameters.

U.S. provisional 62/609,435 titled “Estimating the relationship betweenMAP value and pulse amplitude and methods to achieve so,” discloses onemethod for estimating Ps and Pd for an individual arterial pulse, from aknown value for MAP for that arterial pulse and the waveform for thatarterial pulse, and known values for Ps and Pd for one arterial pulse.

After calibration, tracking sensor data is used to estimate MAP, Ps, andPd for each arterial pulse

The system also includes an estimator for SVV derived from the signalprovided by the tracking sensor.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows system 100, which is a first embodiment of the invention,and an interrelationship of system 100 with a limb of a subject.

FIG. 2 shows system 200, which is a second embodiment of the invention,and an interrelationship of system 200 with a limb of a subject.

FIG. 3 shows system 300, which is a third embodiment of the invention,and an interrelationship of system 300 with a limb of a subject.

FIG. 4 is a schematic of electrical components of tracking transducer102.

FIG. 5 shows a detailed description of hardware assembly 201 of FIGS. 2and 3.

FIG. 6 shows a detailed description of tracking transducer front end 502

FIG. 7 is a flowchart showing algorithm 700 comprising repetitivecalibrate and track activities.

FIG. 8 shows an electrical schematic of a combined electrical model 800including an electrical model (corresponding to a cardiovascular model)804 and a model of a tracking sensor 805.

FIG. 9 is an electrical schematic of one embodiment of element 802 inFIG. 8.

FIG. 10 is an electrical schematic of an alternative embodiment ofelement 802 in FIG. 8.

FIG. 11 is a schematic of a two port network 1100 representing oneembodiment of two-port network 803, of FIG. 8

FIG. 12 shows a waveform containing a sequence of arterial pulses, andindicia helpful in explaining a method of calibration.

FIG. 13 shows two plots; one for values of real components versusharmonic frequency; and one for values of imaginary components versusharmonic frequency, for both tracking data (measurement) and model data,before fitting.

FIG. 14 shows two plots; one for values of real components versusharmonic frequency; and one for values of imaginary components versusharmonic frequency, for both tracking data (measurement) and model data,after fitting.

FIG. 15 is an electrical schematic of circuit 1500 corresponding to acardiovascular model.

FIG. 16 shows arterial pulse trains and time correspondence to asubject's heart SVs; and delta functions.

FIG. 17 is a flow chart showing steps of calibration.

FIG. 18 is a flow chart showing steps of tracking

FIG. 19 is a flow chart showing stroke volume estimation.

DETAILED DESCRIPTION OF EMBODIMENTS

FIG. 1 shows system 100 of a first embodiment and their structuralinterrelationship with arm 101 of a subject. System 100 comprises PCM103, cuff 110, and tracking transducer 102.

Tracking transducer 102 comprises a PPG transducer and is mounted on asubject's finger 106. Cable 107 connects tracking transducer 102 to PCM103. Cuff 110 is mounted around a subject's arm. Two tubes 109 connectcuff 110 to PCM 103. Cuff 110, tubes 109, and PCM 103 comprise anoscillometric cuff based sphygmomanometer. Preferably, trackingtransducer 102 obtains signals from a region of the subject whose bloodflow is not cut off by cuff 110, such as a finger on the opposite are asthe cuff

PCM 103 comprises display 104 and user controls 108.

Display 104 can preferably display graphic representation of biometricdata versus time 104. Biometric data versus time, as shown in FIG. 1,may include arterial pressure. Display 104 can preferably displaynumerical data 105 representing time averages of biometric data.Numerical data 105, as shown in FIG. 1, may include Heart Rate (HR), Ps,Pd, MAP, and SVV.

Controls 108 preferably enable a user to program PCM 103 to graphicallydisplay different biometric data versus time (such as ECG and/orpressure wave), change the time scale of the graphic display, and changethe time or number of arterial pulses used to obtain the time averagednumerical data 105. Controls 108 may also be used to control time delaysbetween sequential calibrations, or to activate immediate calibration.

PCM 103, tubes 109, and cuff 110 enable measurement of pressurevariations, from which Ps, Pd and MAP can be estimated. Measurement ofPs typically occurs a few seconds to less than a minute prior to orafter measurement of Pd, as the cuff deflates or inflates. Preferably,PCM 103 is programmed to determine from the cuff based measurements, avalue for MAP, a value for Ps, and a value for Pd.

PCM 103 comprises at least one numerical processor, such as an Intel™ 17processor. Preferably, this at least one processor executes mathematicalalgorithms on data transduced by cuff 110 and tracking transducer 102.Preferably, this at least one processor determines one or more of HR,Ps, Pd, MAP, and SVV numerical values, and arterial pressure wave, asshown in display 104, from data transduced by cuff 110 and trackingtransducer 102.

FIG. 2 shows physical components of a system 200 and arm 101 of thesubject. System 200 comprises hardware assembly 201, and PCM 103.

Hardware assembly 201 comprises an enclosure separate from an enclosureof PCM 103. Cable 107 connects tracking transducer 102 to PCM 103.Alternatively, cable 107 may contain a branch that has one side from thebranch connecting to hardware assembly 201 and the other side from thebranch connecting to PCM 103. Tubes 109 connect cuff 110 to hardwareassembly 201. Two tubes 203 connect hardware assembly 201 to PCM 103.These tubes communicate pressure between cuff 110 and PCM 103.Alternatively, tubes 109 may contain branches to communicate pressuredirectly to both hardware assembly 201 and PCM 103.

Electrical connection 202 connects hardware assembly 201 to PCM 103.Electrical connection 202 provides unidirectional (from PCM 103 tohardware assembly 201) or bidirectional communication between hardwareassembly 201 to PCM 103.

In the case of unidirectional communication from PCM 103 to hardwareassembly 201, hardware assembly 201 receives from PCM 103 calibrationsensor values (such as values determined from data from cuff 110) andoptionally the tracking sensor values (such as values generated bytracking transducer), and optionally uses electrical connection 204 tocommunicate the estimated pressure wave to the PCM. Wires 204 comprisesfour wires for an analog connection. Wires 204 provide arterial pressurevalues to PCM 103, for example to be displayed.

In case of bidirectional communication between hardware assembly 201 andPCM 103, electrical connection 202 may also send data to the PCM 103.Electrical connection 202 may send to PCM 103 any one or more of dataderived from the calibration sensor (cuff 110) and tracking transducer102 for display on PCM 103. Designs of PCM interfaces to convert data todesired output data formats, such as the data formats required by anyparticular PCM model, are well known. The particular data formatrequired for any particular PCM may be proprietary to any particular PCMmanufacturer. However, given that proprietary format, programming ordesigning of an interface, such that communicates over electricalconnection 202, is well within the ability of anyone skilled in the artand a matter of routine engineering and programming.

Data transferred from hardware assembly 201 to PCM 103 may include anyvalue for display by PCM 103, including time dependent traces andnumerical data. Regarding alerting a person within the presence of thePCM or hardware assembly 201, alerts may be based upon biometricconditions of the subject, or determinations that biometric data isunreliable. For example, hardware assembly 201 or PCM 103 may applyreliability algorithms, which determine when biometric data indicatesunreliability. For example, unreliability may be indicated by a lowsignal to noise ratio of the output signal of the tracking sensor;relatively large changes in data derived from sequential cardiac timeperiods; failure of matching of an arterial pulse to a model thereof(for example due to lack of convergence of a numerical approximationalgorithm). Alerts, for example, may include a sound or visualindicator, and optionally a sound or visual indication of the specificreason for the alert.

PCM 103 of FIG. 2 is similar to PCM 103 of FIG. 1, but also comprises aport connected to line 202, for communicating data to hardware assembly201 from PCM 103. This port serves the purpose of reading thecalibration sensor values and optionally also tracking sensor valuesfrom the PCM. In another embodiment, this connection enablescommunication of estimated BPV values, BPV trace values and alerts, fromthe hardware assembly 201 to PCM 103, via wire 202.

Hardware assembly 201 processes the signals it receives from cuff 110and tracking transducer 102, and optionally signals it receives from PCM103, to generate a digital signal representing arterial pressure for thesubject.

Alternatively, wireless transmitters may replace the wires describedabove for the first and second structural embodiments.

Alternatively, a complete sphygmomanometer (including means forpressurizing and deflating a cuff) may replace cuff 110 described abovefor the first and second structural embodiments, and wire or wirelesstransmitters and/or transceivers may couple this completesphygmomanometer to PCM 103, or PCM 103 and hardware assembly 201. Inthis alternative, elements of a sphygmomanometer in PCM 103 and hardwareassembly 201 are not required.

In the first and second structural embodiments, preferably, PCM 103comprises the pressure driving elements of the sphygmomanometer.

FIG. 3 shows physical components of a system 300 and arm 101 of thesubject. System 300 comprises hardware assembly 201, PCM 103, andexternal display 302.

FIG. 3 shows connection 301 of an external display 302 to hardwareassembly 201. External display 302 may be capable of displaying BPV datafrom hardware assembly 201. Tracking transducer 102 may be connected tohardware assembly 201, to PCM 103, or to both.

FIG. 4 is a schematic of electrical components of tracking transducer102, including light emitting diodes 401 and 402; photodetector PINdiode 403, wires 405 to 410, within cable 107, and authentication device411. This kind of tracking transducer comprises a combination of one ormore light emitting devices and one or more light sensitive devices thatwhen mounted on a subject organ, can detect changes in light absorptionin a part of that organ. Transducer 102 comprises a light source and adetector capable of distinguishing a pulsatile component correspondingto arterial pressure. The DC component of the signal is attributable tothe bulk absorption of the skin tissue, while the AC component isdirectly attributable to variation in blood volume the body organ onwhich it is placed, caused by the pressure corresponding to the cardiaccycle. Typically two light sources are light emitting diodes 401 and402. LED 401 emits infrared light with wavelength of 940 nm, and LED 402emits red light, with wavelength of 660 nm. These wavelengths aretypical value, and other wavelengths can be used in the infrared andvisible regions, including greed light which is also sometimes used. Thetransducer also includes a photodetector PIN diode 403. The trackingtransducer optionally also includes an authentication device 411 whichprovides the transducer with a unique ID. This arrangement, togetherwith appropriate provision in assembly 201, will safeguard the subjectfrom being fit with a transducer that was used on another subjectbeforehand. Optional authentication device 411 comprises an integratedcircuit ROM programmed with a unique ID and having a single contact onewire interface, like DS28E05 by Maxim Semiconductors.

Tracking transducer 102 connects via cable 107 to a suitable interface.Cable 107 typically comprises 4 or 6 wires. One pair of wires (405,406)for the light sources, one pair (407,408) for the photodetector andoptionally a pair (409,410) for the authentication device.

FIG. 5 shows hardware assembly 201 including pressure sensor 501;tracking transducer front end 502; processing system 503; digital toanalog (D/A) converter 505; interface to PCM 504; and display interface506. All these circuit blocks are interconnected via digital bus 507.

Circuit blocks: pressure sensor 501; tracking transducer front end 502;display interface 506; and D/A converter 505 are optional. Pressuresensor 501 senses the air pressure provided in cuff 110. PPG front end502 interfaces to the tracking transducer 102 and provides and interfaceto the processing system 503. Processing system 503 may run real-timeBPV and/or SVV estimation algorithms. Processing system 503 maycommunicate BPV and/or SVV data to one or more of interface circuit 504;D/A converter 505; and display interface 506.

In embodiments, interface circuit 504 reads the calibration dataprovided by the PCM 103 and optionally also the data sent by thetracking transducer 102 to the PCM 103. In embodiments, the trackingtransducer interfaces to assembly 201 directly, and interface to PCM 504interfaces to PCM 103 for reading the calibration data. In embodiments,interface to PCM 504 sends the estimated pressure values to PCM 103. Inone embodiment, this data is sent to PCM 103 in analog form using D/Aconverter 505. In embodiments, interface circuit 504 converts BPV and/orSVV data to a form compatible with PCM 103, and transmits the formallycompatible data via wire 202 to PCM 103. Interface circuit 304 mayformat data for transmission serial RS232 connection, USB, Ethernet(LAN), or any other data format in which PCM 103 is capable of receivingBPV and SVV data.

In case of bidirectional communication between hardware assembly 201 andPCM 103, interface 504 may also send data to PCM 103. Interface 504 maysend to PCM 103 any one or more of data derived from the calibrationsensor (cuff 110) and tracking transducer 102 for display on PCM 103.PCM Designs of interfaces to convert data to desired output dataformats, such as the data formats required by any particular PCM model,are well known. The particular data format required for any particularPCM may be proprietary to any particular PCM manufacturer. However,given that proprietary format, programming or designing of an interface,such interface 504, is well within the ability of anyone skilled in theart and a matter of routine engineering and programming.

FIG. 6 shows a tracking transducer interface circuit 502. When thetracking transducer is connected with the tracking transducer interface,together they provide the functionality of a photoplethysmographicsensor, which is typically used to monitor the perfusion of blood in thesubject tissue.

Tracking transducer interface circuit 502 comprises transimpedanceamplifier 601; filter circuit 602; analog to digital (A/D) converter603; LED driver 604; current control D/A converter 605; and Digitalinterface circuit 606.

LED driver 604 drives current pulses to the LED's. The current of thesepulses is controlled by a current control DAC 605, which in turn iscontrolled by digital interface circuit 606. The signal from thephotodetector 403 is amplified by a transimpedance amplifier 601, isfiltered by filter circuit 602 and is sampled by A/D digital converter603. The signal from 603 is connected to digital interface circuit 606.Digital interface circuit 606 connects to the processor via bus 507. Inthe case where cable 107 contains a branch that has one side from thebranch connecting to hardware assembly 201 and the other side from thebranch connecting to PCM 103, LED driver 604 and current control D/Aconverter 605 are not needed and may not be implemented.

Combined Electrical Model

FIG. 8 shows a combined electrical model 800, comprising cardiovascularsystem electrical model 804 and sensor system model 805.

Cardiovascular system electrical model 804 comprises current source 801;load 802; two-port network 803; equipotential potential connection 807between output of current source 801 and both input of load 802 andtwo-port network 803.

Sensor system model 805 defines another two-port network. Sensor systemmodel 805 has an input having an equipotential with an output oftwo-port network 803. All reference terminals of elements 801; 802; 803;and 805 are referenced to a common ground.

Output 806 of sensor system model 805 is the output of combinedelectrical model 800.

The frequency domain output signal of the combined electrical model 800is defined by:

Y(w)=N*Xh(w)*Zl(w,MAP)*Hx(w)*Hs(w), where:  (28)

w represents frequency;

N is a real number;

Xh(w) represents the current produced by current source 801.

Zl(w, MAP) represents the input impedance of load 802.

Hx(w) represents the transfer function of two-port 803, having aninfinite input impedance.

Hs(w) represents the transfer function of two-port 805.

Xh models pumping of the heart. Zl models impedance of major arteries;Hx models transfer of arterial pressure output near the heart toarterial pressure at pressure measurement location; Hs models changefrom arterial pressure at the measurement location to tracking sensoroutput signal.

The asterisk (*) represents multiplication; w represents frequency; andMAP is defined above. The model assumes that Zl is the only MAPdependent function.

For MODEL1(w) is the frequency domain output signal of MODEL1:

$\begin{matrix}{{{{MODEL}\; 1(w)} = {\frac{1}{X{h(0)}*Z1(0)*H{x(0)}*H{s(0)}}*X{h(w)}*Z1(w)*H{x(w)}*{{Hs}(W)}}},} & (29)\end{matrix}$

where:

MODEL1 represents the output signal from the combined electrical model,as described in the First Normalization and Fitting Method herein above.

For MODEL2(w) is the frequency domain output signal of MODEL2:

$\begin{matrix}{{{{MODEL}\; 2(w)} = {\frac{1}{{{X_{h}\left( w_{1} \right)}*{Z_{1}\left( w_{1} \right)}*{H_{x}\left( w_{1} \right)}*{H_{s}\left( w_{1} \right)}}}*{X_{h}(w)}*{Z_{1}(w)}*{H_{x}(w)}*{H_{s}(w)}}},} & (30)\end{matrix}$

where:

Xh(w) is the heart function 801 of FIG. 8;

w1 is the frequency of the first harmonic of the arterial pulse that ismodeled;

Zl(w) is the heart load impedance represented by load 802 in FIG. 8;

Hx(w) is the heart to fingertip transfer function; and

Hs(w) is the transfer function of the tracking sensor front end.

One option for Xh(w) is:

$\begin{matrix}{{{XH}(w)} = {\mathcal{F}\left( {e^{({\Gamma*t})}*\left( {1 + \frac{t}{FT}} \right)*t} \right)}} & (31)\end{matrix}$

In this equation, Γ and FT are the model parameters, and represents aDiscrete Fourier Transform (DFT).

The inventor has discovered that a fixed value of F between 3.0 and 9.0,and preferably Γ equals 6.154 is sufficient for tracking of BPV.

FT is one of the model parameters.

In embodiments, the heart function is unity: Xh(w)=1, representing theFourier transform of a Dirac delta function.

In embodiments, Xh(w) a Fourier transform of a triangular wave:

$\begin{matrix}{{{Xh}(w)} = {\mathcal{F}\left\{ \begin{matrix}{{1 - {\alpha \; t\mspace{14mu} {for}\mspace{14mu} 0}} < t \leq \frac{1}{\alpha}} \\{0\mspace{14mu} {otherwise}}\end{matrix} \right.}} & (32)\end{matrix}$

α is a model parameter. In embodiments, a value for a is determinedduring calibration. In embodiments, a value for a is determined duringtracking.

Hs is the transfer function of two port network 805 of FIG. 8. Two portnetwork 805 may comprises a low pass filter providing a finite durationoutput (FIR filter) and a high pass filter whose response does notbecome zero at any finite time (IIR filter).

FIG. 9 shows an electrical schematic of one embodiment load 802 in FIG.8.

Load 802 comprises resistor 902, inductor 903, capacitor 904, andresistor 905. Resistors 902, 904 are referenced to common ground andresistor 902 and inductor 903 are connected to equipotential potentialconnection 807. The value of capacitor 904 correspond to acardiovascular model in which the capacitance is MAP dependent, andvaries as 1/MAP.

For the FIG. 9 schematic:

$\begin{matrix}{{{Z_{1}(w)} = {\frac{S^{2} + {\frac{w_{0}({MAP})}{Q}*S} + {w_{0}^{2}({MAP})}}{S^{2} + {{w_{0}^{2}({MAP})}*\tau*S} + {w_{0}^{2}({MAP})}}e^{s*T_{s}}}},} & (33)\end{matrix}$

where

=j*w;

and w₀, Q, and τ are model parameters;

Ts is a parameter representing a time difference between a determinedtime at which the corresponding cardiac cycle begins and when Systolebegins and, and w₀, is the zero frequency.

In another embodiment, the Z₁ is defined as:

$\begin{matrix}{{{Z_{1}(w)} = {\frac{S^{2} + {\frac{w_{01}({MAP})}{Q}*S} + {w_{01}^{2}({MAP})}}{S^{2} + {{w_{02}^{2}({MAP})}*\tau*S} + {w_{02}^{2}({MAP})}}e^{s*T_{s}}}},} & (34)\end{matrix}$

where:

w01, w02, Q, τ, and Ts are model parameters that are determined byfitting.

FIG. 10 shows an electrical schematic of an alternative embodiment ofload 802 in FIG. 8. In FIG. 10, load 802 comprises transmission line1001 and termination 1002. Termination 1002 comprises capacitor 1003 andresistor 1003 in parallel across the transmission line 1001.

The input impedance to load 802 is:

$\begin{matrix}{{Z\; 1} = {Z_{0}\frac{{Z\; t} + {j*Z_{0}{\tan \left( {\beta \; L} \right)}}}{Z_{0} + {j*Z\; t*{\tan \left( {\beta \; L} \right)}}}}} & (35)\end{matrix}$

where:

Z₀ is a function of MAP;

Zt is the termination impedance defined by the capacitor 1003 andresistor 1003 in parallel across the transmission line 1001;

β is a function of w and MAP; and

L is length of transmission line 1001.

In embodiments, Z₀ is proportional to sqrt(MAP).

In embodiments, Beta is proportional to w*sqrt(MAP).

In embodiments, the capacitance of capacitor 103 is proportional to1/MAP.

FIG. 11 shows a schematic of a two port network 1100 representing oneembodiment of two-port network 803, of FIG. 8. Two port network 1100comprises input 1103 and output 1104, each comprising two terminals,transmission line 1101, and termination 1102. V1 and V2 representvoltages at the input and output respectively.

The transfer function for FIG. 11 is one embodiment of Hx(w). Thistransfer function is:

$\begin{matrix}{{{{Hx}(w)} = {\frac{V_{2}(w)}{V_{1}(w)} = \frac{1 + \Gamma}{{e^{j*w*t}d} + {\Gamma*e^{{- j}*w*t_{d}}}}}},} & (36)\end{matrix}$

where:

t_(d), Γ, are constants.

FIG. 12 shows waveform 1201, time 1202, arterial pulse 1203, andwaveform segment 1204 of waveform 1201. FIG. 12 shows waveform segment1204 spanning a sequence of 5 arterial pulses. All arterial pulses inwaveform segment 1204 are relatively close in time, to time 1202.Waveform segment 1204 illustrates a time period over which systems 100,200, 300 may use tracking data for calibration. The five arterial pulsesshown in waveform segment 1204 are for illustrative purposes only. Moreor fewer arterial pulses from the tracking data may be used, so long astracking data for at least one arterial pulse is used. Waveform 1201represents data from the tracking transducer waveform segment 1204 showsa segment containing plural arterial pulses. Waveform 1201 shows semirepetitive arterial pulses which correspond to arterial pressure changesin the location of the subject's body monitored by the tracking sensor,and also correspond to the periods of cardiac cycles. Each arterialpulse shows two maxima separated by a minima corresponding to thedicrotic notch, and with the first maxima higher than the second maxima.Waveform 1201 is for purposes of illustrating the invention andtherefore shows relatively identical arterial pulses. Actual arterialpressure waveforms typically have cardiac pulse periods and amplitudesthat substantially vary from one another.

Preferably, arterial pulses from the tracking data used for calibrationoccur within 10 minutes of time 1202, more preferably within 1 minute oftime 1202, more preferably within 20 seconds of time 1202, and mostpreferably within 10 seconds of time 1202 including the arterial pulseoverlapping in time with time 1202.

Time 1202 identifies time 1202 that PCM 103 or hardware assembly 201determined to be the time at which the calibration sensor determinedcalibration values Ps, Pd, or MAP values. In embodiments, the processingsystem determines a time at which the calibration sensor obtained dataused for determining Ps, Pd, or MAP, and identifies the arterial pulsein the tracking data closest to that time. For example, pulse 1203spanning time 1202. The processing system uses the data from this pulse1203 in the calibration process. In other embodiments, the processingsystem uses the data for pulse 1203 and other pulses, such as theadjacent pulses, in the calibration process, or all pulses in waveformsegment 1204.

In one embodiment, arterial pulse 1203 is identified as the oneproducing the largest pressure fluctuation during one cardiac cycle inthe pressure sensor 501 or by PCM 103. During calibration, this arterialpulse frequency content and the calibration values are used to train amodel and find the parameters of the model that match the measuredsignal as closely as possible.

In embodiments which incorporate a cuff of the form used for bloodpressure measurement, the processing system may determine the point intime at which the variation of pressure with time is the largest, duringone cardiac cycle. The processing system may use tracking sensor dataclose to this time, as discussed above, for calibration.

FIG. 13 shows two plots; one for values of real components versusharmonic frequency; and one for values of imaginary components versusharmonic frequency, for both tracking data (measurement) and model data,before fitting.

FIG. 13's upper plot shows values of real components versus harmonicfrequency for tracking data (measurement) and model data. FIG. 13'slower plot shows values of imaginary components versus harmonicfrequency for tracking data (measurement) and model data. FIG. 13 showsthe data, before fitting the selected model to the tracking data. FIG.13 shows harmonics along the x axis. The frequencies of these harmonicsare integers divided by the cardiac pulse period.

FIG. 13 shows values for the DC component and the harmonic frequenciesfor values 1, 2, and 3 times the fundamental frequency, for the model.

FIG. 13 shows values for the fundamental frequency and harmonics at 2and 3 for the tracking data (obtained during one cardiac time period andfor the time duration of cardiac time period). FIG. 13 show no DC valuefor tracking data and DC value of tracking data is not used by theprocessing system.

FIG. 14 shows two plots; one for values of real components versusharmonic frequency; and one for values of imaginary components versusharmonic frequency, for both tracking data (measurement) and model data,after fitting.

FIG. 14 has an upper plot which shows values of real components versusharmonic frequency for tracking data (measurement) and model data. FIG.14 has a lower plot which shows values of imaginary components versusharmonic frequency for tracking data (measurement) and model data.

FIGS. 13 and 14 show data for the same pulse and therefore for harmonicsthat have the same frequencies. FIG. 14 shows the data, after fitting.FIG. 14 shows values for the DC component of the model, and values forthe harmonics 1, 2, and 3 times the fundamental frequency for both themodel and the tracking data. FIG. 14 shows model data that is a best fitto the values of the tracking data harmonics 1, 2, and 3 times thefundamental frequency.

In some embodiments, for fitting for a calibration, w₀, Q, τ, FT and Tsare allowed to vary to obtain a best fit.

In some embodiments, for tracking, T and Ts are fixed, and w₀, Q, τ, FTare allowed to vary to obtain a best fit. In this case, T and Ts arefixed values that are functions of values for T and Ts determined duringcalibration.

FIG. 15 shows an electrical schematic of circuit 1500 corresponding to acardiovascular model. This model may be used as the basis to determinePP during tracking. FIG. 15 shows electrical circuit 1500 comprisingcurrent source 1501, resistor 1502, and capacitor 1503, and grounds1504. R resistor 1502 and capacitor 1503 are in parallel and referencedto ground 1504. FIG. 15 has a response versus frequency that is afunction that has a single pole. At low frequencies up to thefundamental harmonic of the heart, the cardiovascular system can beconsidered as a single pole system.

Electrical circuit 1500 is a simplified single pole model that may beused by the processing system to determine T_(Z) (defined herein below)during calibration. During tracking, the processing system may useT_(Z), MAP and PP determined from calibration, and the MAP estimatedduring tracking, to calculate PP during tracking.

Electrical circuit 1500 has a ratio of the amplitude of the firstharmonic, H1, to the DC amplitude, H0, of:

$\begin{matrix}{{\frac{H1}{H0} = {{abs}\mspace{11mu} \left( \frac{1}{\left( {R*C*S} \right) + 1} \right)}},} & (37)\end{matrix}$

where:

R is the resistance of resistor 1502;

C is the capacitance of capacitor 1503;

S=j*w where w is angular frequency.

In the corresponding cardiovascular model, C is proportional to 1/MAP.In the corresponding cardiovascular model, PP/MAP=(H1/H0)*K, where K isthe number specified in the formula for FSUB. Consequently, thiselectrical model enables determination of PP for the correspondingcardiovascular model.

MAP and PP values are determined during calibration, to provide MAP1 andPP1. Using these values, τ₁ can be calculated as follows:

$\begin{matrix}{{\tau_{1} = \sqrt{\frac{{K^{2}*\left( \frac{{MAP}_{1}}{{PP}_{1}} \right)^{2}} - 1}{w_{1}^{2}}}},} & (38)\end{matrix}$

where

K is the constant defined above;  (39)

${{w1} = \frac{2*\Pi}{IBI_{1}}};$

and

IBI₁ is the cardiac time period of the other arterial pulse.

PP2 is the estimation of PP for the particular arterial pulse havingMAP2.

$\begin{matrix}{{{{PP}\; 2} = {{PP}\; 1*\frac{{MAP}_{2}}{{MAP}_{1}}\sqrt{\frac{\left( {\tau_{1}*w_{1}} \right)^{2} + 1}{\left( {\tau_{1}*\frac{{MAP}_{2}}{{MAP}_{1}}*w_{2}} \right)^{2} + 1}}}},} & (40)\end{matrix}$

where:

MAP 2 is estimated according to the map tacking method above;

${{w2} = \frac{2*\Pi}{IBI_{2}}};$

and

IBI₂ is the cardiac time period of the particular arterial pulse.

In a different embodiment, unrelated to FIG. 15, the processing systemmay calculate PP2 assuming the following relationship:

$\begin{matrix}{{{PP}\; 2} = {{PP}\; 1*\frac{{MAP}_{2}}{{MAP}_{1}}}} & (41)\end{matrix}$

FIG. 16 shows arterial pulse trains and time correspondence to asubject's heart SVs; and delta functions.

FIG. 16 shows traces 1601, 1602, and delta functions 1603; marker 1604;and time difference deltaT, 1605.

Trace 1601 shows a resultant arterial pressure versus time. Trace 1602represents heart blood flow versus time. Magnitudes of delta functions1603 represent values for heart stroke volume at times equal to the endof each diastole phase. Marker 1604 identifies times which theprocessing system determines from tracking sensor data to be thebeginning of cardiac cycles. Marker points 1604 can be identified fromthe characteristic features as described above in the fourth step ofcalibration: “PROCESSING TRACKING SENSOR DATA.” Time difference 1605identifies time deltaT between end of diastole and marker point 1604.

Relating Processing to Cardiovascular System

The processing system uses the data shown in FIG. 16 to determine startand end times of cardiac cycles. The processing system uses cardiaccycle start and end times, trace 1601, and a particular cardiovascularmodel to determine one value for deltaT and the SVs of the cardiaccycles, as described above in the discussion of SV estimation.

The SV estimation process described above is based upon this particularcardiovascular model. This cardiovascular model assumes heart blood flowversus time is a convolution of the series of variable amplitude deltafunctions, shown by 1603, with a heart function xh(t). For example,xh(t) may be defined by the argument of the Fourier transform ofequation (31), which is:

$\begin{matrix}{{{xh}(t)} = {e^{({\Gamma*t})}*{\left( {1 + \frac{t}{FT}} \right).}}} & (42)\end{matrix}$

The Fourier Transform of the Heart Blood Flow (hbf) versus time is:

HBF(w)=Σ_(i=0) ^(N−1) Xh)(w))*SVi*e ^(−S*t) ^(i) , where:  (43)

Xh(w) is taken from equation (31);

SVi are the stroke volumes of the i=0, . . . , N−1 stroke volumes, SV.

S=j*w; and

t_(i) are the instances of impulse i of the delta functions.

The arterial pressure versus time is merely another convolution of thehbf with the impulse response of the corresponding combined electricalmodel comprising load 802; two-port network 803 and tracking sensor 805of FIG. 8.

In the frequency domain this can be expressed following equation (29)as:

Y(w)=HBF(w)*Hsys(w)  (44)

Where Hsys(w) is defined as:

Hsys(w)=Zl(w)Hx(w)Hs(w)  (45)

And therefore the equations connecting the stroke volumes to thespectrum of the signal Y(w) as measured by the sensor is:

Y(w)=e ^(−S*Δt) *Hsys(w)Σ_(i=0) ^(N−1)SV_(i) *e ^(−S*t) ^(i)   (46)

Both Y(w) and Hsys(ωw) are vectors, that is a series of values,preferable complex, with length equal to the length of the unknown SV,which is also a vector, which is a list of values, preferably real. Wecan therefore rewrite equation (46) as:

$\begin{matrix}{\frac{Y(w)}{Hsy{s(w)}} = {e^{{- S}*{delta}\; T}{\sum_{i = 0}^{N - 1}{{SV}_{i}*e^{{- S}*t_{i}}}}}} & (47)\end{matrix}$

We can equation (47) in matrix notation:

$\begin{matrix}{{{{\lbrack L\rbrack \lbrack M\rbrack}\left\lbrack {SV} \right\rbrack} = {\frac{\lbrack Y\rbrack}{\left\lbrack {Hsys} \right\rbrack} = \lbrack R\rbrack}},} & (48)\end{matrix}$

where we have defined:

$\begin{matrix}{{\lbrack R\rbrack = \frac{\lbrack Y\rbrack}{\left\lbrack {Hsys} \right\rbrack}},} & (49)\end{matrix}$

and where M is a matrix of the form

$\begin{matrix}{\lbrack M\rbrack = \begin{matrix}e^{{- j}*t_{1}*w_{1}} & e^{{- j}*t_{2}*w_{1}} & e^{{- j}*t_{3}*w_{1}} \\e^{{- j}*t_{1}*w_{2}} & e^{{- j}*t_{2}*w_{2}} & e^{{- j}*t_{3}*w_{2}} \\e^{{- j}*t_{1}*w_{3}} & e^{{- j}*t_{2}*w_{3}} & e^{{- j}*t_{3}*w_{3}}\end{matrix}} & (50)\end{matrix}$

L is a diagonal matrix representing the time shift,

L=diag(e ^(−j*Δt*w) ¹ ,e ^(−j*Δt*w) ² ,e ^(−j*Δt*w) ³ , . . . )

SV is an array of real SV values, Hsys is as defined in equation (45),and Y(w) is the measured signal at the output.

The system dimension N is the number of arterial pulses in the segmentto be analyzed. This is also the number of frequencies at which toperform the analysis.

However, we have N complex equations and N+1 real unknowns. These arethe N dimension real vector SV and the real values deltaT.

To solve the system of equations for SV we shall minimize the imaginarypart of the SV's by minimizing their sum of squares, by finding the timeshift deltaT that minimize the error function:

err=Σ_(i=0) ^(N−1)(im(SV_(i)))², using a minimization algorithm,for  (51)

example L-BFGS-B where SV_(i) are result of solving equation (48) forSV.

In one embodiment, the solution for equation (48) is:

$\begin{matrix}{\left\lbrack {SV} \right\rbrack = {{\lbrack M\rbrack^{- 1}\lbrack L\rbrack}^{- 1}\frac{\lbrack Y\rbrack}{\left\lbrack {Hsys} \right\rbrack}}} & (52)\end{matrix}$

As the frequency domain signal arises from a DFT on an analog signalwith an integer number arterial pulses, the N frequencies will bespanned equally, w[n+1]−w[n]=w[n]−w[n−1].

For best quality estimation, the N frequencies to use for solutionshould be where the signal is strongest, and this occurs around the meanheart rate frequency of the analyzed segment. As N frequencies aroundthis mean frequency are required, it is necessary to include thefrequencies F=[HR/2, HR/2+HR/N, HR/2+2*HR/2 . . . 3/2*HR−HR/N] or asmall shift of a couple of HR/N from this raster. Practically, thefrequency raster is recommended to be between HR/4 to 7/4*HR.

It should be noted, that while the analysis uses a model [Hsys] of thecardiovascular system to solve for the unknown SV, the actual resultsare insensitive to the exact values of [Hsys]. Therefore, even asufficient educated guess for the values of this model are sufficient toachieve a good quality estimation of SV.

A system for estimating a ratios of SVs or blood pressure, or both,comprising:

a processing system comprising a processing unit and memory;

the processing system is designed to receive calibration sensor datafrom a calibration sensor;

the processing system is designed to receive tracking sensor data from atracking sensor;

the processing system is designed to determine a normalization valuebased upon a function of the calibration sensor data and the trackingsensor data;

and

the processing system is designed to divide at least one harmonic valueof the tracking sensor data by the normalization value.

1. A system for estimating values of hemodynamic parameters of asubject, comprising: a processing system comprising a processing unitand memory; wherein the processing system is designed to receivecalibration sensor data that relates to arterial pressure from acalibration sensor; wherein the processing system is designed to receivetracking sensor data from a tracking sensor; the processing system isdesigned to calculate estimated hemodynamic values of a hemodynamicparameter based upon: one or more outputs of a DFT of tracking sensordata relating to the arterial pressure, and which tracking sensor datawas obtained from the subject during a calibration time period; at leasttwo of MAP, PP, Ps, and Pd values from data obtained from the subjectduring the calibration time period; one or more outputs of a DFT oftracking sensor data relating to the arterial pressure, which trackingsensor data was obtained during a tracking time period; and wherein thetracking time period is different from the calibration time period;wherein the processing system is designed to display, store or transmitthe estimated hemodynamic values. 2-18. (canceled)
 19. A system forestimating a ratio of SV values of a subject, comprising: a processingsystem comprising a processing unit and memory; wherein the processingsystem is designed to receive tracking sensor data from a trackingsensor data that relates to changes in arterial pressure; the processingsystem is designed to estimate a ratio of SV values, based upon: one ormore outputs of a DFT of tracking sensor data relating to the arterialpressure; and wherein the processing system is designed to store ortransmit said ratio of SV values.
 20. The system of 19, wherein: theprocessing system is designed to determine parameters of a combinedelectrical model that corresponds to a cardiovascular model, by acalibration fitting of a function of the combined electrical model to afunction of output of a DFT of tracking sensor data for data from acalibration time period.
 21. The system of claim 19 further comprising:a calibration sensor; a tracking sensor; and a device for visuallydisplaying or transmitting values for hemodynamic parameters.
 22. Thesystem of claim 19: wherein the processing system is designed todetermine SVV from ratio of SV values.
 23. A system for estimatingvalues of hemodynamic parameters of a subject, comprising: a processingsystem comprising a processing unit and memory; wherein the processingsystem is designed to determine a calibration value for at least of MAP,PP, Ps, and Pd from calibration sensor data obtained from a subject;wherein the processing system is designed to calculate an FSUB valuefrom a function of variables comprising: MAP; PP; and a value of aharmonic of a DFT of tracking sensor data obtained from the subject;wherein the processing system is designed to calculate hemodynamicvalues of at least one hemodynamic parameter using said FSUB value andsaid calibration value; and wherein the processing system is designed tostore or transmit the calculated hemodynamic values.
 24. A system forestimating values of hemodynamic parameters of a subject, comprising: aprocessing system comprising a processing unit and memory; wherein theprocessing system is designed to receive tracking sensor data from atracking sensor; wherein the processing system is designed to calculateestimated hemodynamic values of a hemodynamic parameter at two or moretime instances, based upon: one or more outputs of a DFT of trackingsensor data relating to the arterial pressure, which tracking sensordata was obtained from the subject during a first tracking time period;one or more outputs of a DFT of tracking sensor data relating to thearterial pressure, which tracking sensor data was obtained from thesubject during a second tracking time period; wherein the first trackingtime period and the second tracking time period do not overlap in time;and wherein the processing system is designed to display, store ortransmit data relating to the estimated hemodynamic values. 25.(canceled)
 26. A method for estimating a ratio of SV values of asubject, using a system comprising a processing system comprising aprocessing unit and memory, comprising: receiving in the processingsystem tracking sensor data from a tracking sensor data that relates tochanges in arterial pressure; the processing system estimating a ratioof SV values, based upon one or more outputs of a DFT of tracking sensordata relating to the arterial pressure; and the processing systemstoring or transmitting said ratio of SV values. 27-28. (canceled)